Simplify the following expression: $ t = \dfrac{-3z - 9}{6} + \dfrac{-7}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-3z - 9}{6} \times \dfrac{4}{4} = \dfrac{-12z - 36}{24} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-7}{4} \times \dfrac{6}{6} = \dfrac{-42}{24} $ Therefore $ t = \dfrac{-12z - 36}{24} + \dfrac{-42}{24} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-12z - 36 - 42}{24} $ $t = \dfrac{-12z - 78}{24}$ Simplify the expression by dividing the numerator and denominator by 6: $t = \dfrac{-2z - 13}{4}$